Theory and numerics of geometrically non-linear gradient plasticity

International Journal of Engineering Science

Volumn 41, Issue 13-14, 2003, Pages 1603-1629

  Liebe, Tina ^a   Menzel, Andreas ^a   Steinmann, Paul ^a  

^a Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

Author keywords

FEM; Gradient plasticity; Large deformations

Indexed keywords

ALGORITHMS; COMPUTATIONAL GEOMETRY; CONVERGENCE OF NUMERICAL METHODS; DRAG; FINITE ELEMENT METHOD; HARDENING; NONLINEAR PROGRAMMING; PLASTICITY; STRAIN; STRESS ANALYSIS; THERMODYNAMICS;

NON-LINEAR GRADIENT PLASTICITY;

CONTINUUM MECHANICS;

EID: 0038018660     PISSN: 00207225     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7225(03)00030-2     Document Type: Conference Paper

References (45)

1. Aifantis E. On the role of gradients in the localization of deformation and fracture. Int. J. Eng. Sci. 30:1992;1279-1299.
2. Steinmann P. Views on multiplicative elastoplasticity and the continuum theory of dislocations. Int. J. Eng. Sci. 34:1996;1717-1735.
3. Menzel A., Steinmann P. On the continuum formulation of higher gradient plasticity for single and polycrystals. J. Mech. Phys. Solids. 48:2000;1777-1796 Erratum. 49:2001;1179-1180.
4. Cermelli P., Gurtin M. On the characterization of geometrically necessary dislocations in finite plasticity. J. Mech. Phys. Solids. 49(7):2001;1539-1568.
5. Hall E. The deformation and aging of mild steel. Proc. Phys. Soc. B. 64:1951;747-753.
6. Petch N. The cleavage strength of polycrystals. J. Iron Steel Inst. 174:1953;25-28.
7. Kocks U. Polyslip in single crystals. Acta Metallurgica. 8:1960;345-352.
8. Ashby M. The deformation of plastically non-homogeneous materials. Phil. Mag. 21:1970;399-424.
9. Amelinckx S. Dislocations in particular structures. Nabarro F. Dislocations in Solids (Dislocations in Crystals). Vol. 2:1979;67-460 North-Holland Publishing Company, Amsterdam.
10. Fleck N., Muller G., Ashby M., Hutchinson J. Strain gradient plasticity: theory and experiment. Acta Metall. Mater. 42:1994;475-487.
11. Fleck N., Hutchinson J. Strain gradient plasticity. Adv. Appl. Mech. 33:1997;295-361.
12. Capriz G. Continua with Microstructure. 1989;Springer-Verlag, Berlin.
13. Mariano P. Multifield Theories in Mechanics of Solids. Advances in Applied Mechanics. Vol. 38:2002;1-93 Academic Press, New York.
14. Cosserat E., Cosserat F. Sur la theorie des corps deformables. 1909;Duod, Paris.
15. Maugin G. The Thermomechanics of Nonlinear Irreversible Behaviors. 1999;World Scientific Publishing Co. Pvt. Ltd, Singapore.
16. Bažant Z., Pijaudier-Cabot G. Nonlocal continuum damage, localization instability and convergence. ASME J. Appl. Mech. 55:1988;287-293.
17. Sluys L., de Borst R., Mühlhaus H. Wave propagation localization and dispersion in a gradient-dependent medium. Int. J. Solids Struct. 30:1993;1153-1171.
18. J. Pamin, Gradient-dependent plasticity in numerical simulation of localization phenomena, Ph.D. dissertation, Delft University of Technology, Delft, 1994.
19. de Borst R., Pamin J. Some novel developments in finite element procedures for gradient-dependent plasticity and finite elements. Int. J. Numer. Meth. Eng. 39:1996;2477-2505.
20. Peerlings R., de Borst W., Brekelmans R., de Vree J. Gradient enhanced damage for quasi-brittle materials. Int. J. Numer. Meth. Eng. 39:1996;3391-3403.
21. Peerlings R., de Borst R., Brekelmans W., de Vree J. Some observations on localization in non-local and gradient damage models. Eur. J. Mech. A/Solids. 15:1996;937-953.
22. Mikkelsen L. Post-necking behaviour modelled by a gradient dependent plasticity theory. Int. J. Solids Struct. 34:1997;4531-4546.
23. Steinmann P. Formulation and computation of geometrically non-linear gradient damage. Int. J. Numer. Meth. Eng. 46:1999;757-779.
24. Comi C. Computational modelling of gradient-enhanced damage in quasi-brittle materials. Mech. Cohes.-Frict. Mater. 4:1999;17-36.
25. Chambon R., Caillerie D., El Hassan N. One-dimensional localisation studied with a second grade model. Eur. J. Mech. A/Solids. 17:1998;637-656.
26. Svedberg T., Runesson K. An algorithm for gradient-regularized plasticity coupled to damage based on a dual mixed FE-formulation. Comput. Meth. Appl. Mech. Eng. 161:1998;49-65.
27. T. Svedberg, On the modeling and numerics of gradient-regularized plasticity coupled to damage, Ph.D. thesis, Chalmers University of Technology, Göteborg, Sweden, 1999.
28. Nedjar B. Elastoplastic-damage modelling including the gradient of damage. Formulation and computational aspects. Int. J. Solids Struct. 38:2001;5421-5451.
29. Pinsky P. A finite element formulation for elastoplasticity based on a three-field variational equation. Comput. Meth. Appl. Mech. Eng. 61:1986;41-60.
30. Simo J., Kennedy J., Taylor R. Complementary mixed finite element formulations for elastoplasticity. Comput. Meth. Appl. Mech. Eng. 74:1989;177-206.
31. Florez-Lopez J., Benallal A., Geymonat G., Billardon R. A two-field finite element formulation for elasticity coupled to damage. Comput. Meth. Appl. Mech. Eng. 114:1994;193-212.
32. Liebe T., Steinmann P. Theory and numerics of a thermomechanically consistent framework for geometrically linear gradient plasticity. Int. J. Numer. Meth. Eng. 51:2001;1437-1467.
33. Kosevich A. Crystal dislocations and the theory of elasticity. Nabarro F. Dislocations in Solids (The Elastic Theory). Vol. 1:1979;33-141 North-Holland Publishing Company, Amsterdam.
34. Truesdell C., Noll W. The Non-Linear Field Theories of Mechanics. 2nd Edition:1992;Springer, Berlin.
35. Shizawa K., Zbib H. A thermodynamical theory of gradient elastoplasticity with dislocation density tensor. I. Fundamentals. Int. J. Plasticity. 15:1999;899-938.
36. Acharya A., Bassani J. Lattice incompatibility and the gradient theory of crystal plasticity. J. Mech. Phys. Solids. 48(8):2000;1565-1595.
37. Bažant Z. Why continuum damage is nonlocal: micromechanics arguments. ASCE J. Eng. Mech. 117:1991;1070-1087.
38. Aifantis E. On the microstructural origin of certain inelastic models. J. Eng. Mater. Technol. 106:1984;326-330.
39. Polizzotto C., Borino G. A thermodynamics-based formulation of gradient-dependent plasticity. Eur. J. Mech. A/Solids. 17:1998;741-761.
40. Edelen D., Laws N. On the thermodynamics of systems with nonlocality. Arch. Rat. Mech. Anal. 43:1971;24-35.
41. Steinmann P., Stein E. On the numerical treatment and analysis of finite deformation ductile single crystal plasticity. Comput. Meth. Appl. Mech. Eng. 129:1996;235-254.
42. Miehe C. Exponential map algorithm for stress updates in anisotropic multiplicative elastoplasticity for single crystals. Int. J. Numer. Meth. Eng. 39:1996;3367-3390.
43. Le K., Stumpf H. Strain measures, integrability condition and frame indifference in the theory of oriented media. Int. J. Solids Struct. 35(9):1998;783-798.
44. Miehe C., Schröder J., Schotte J. Computational homogenization analysis in finite plasticity simulation of texture development in polycrystalline materials. Comput. Meth. Appl. Mech. Eng. 171:1999;387-418.
45. Simo J. Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory. Comput. Meth. Appl. Mech. Eng. 99:1992;61-112.